Related papers: Examples of quantum integrals
This is a course on the theory of quantum computing. It consists of 16 lessons, each with a video and written component, covering the basics of quantum information, quantum algorithms (including query algorithms, Shor's algorithm for…
The Fundamental Theorem of Integral Calculus links the integrand and its antiderivative via a simple first order differential equation. A numerical solution of this ode yields the antiderivative and hence the required integral. This…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in…
We introduce the notions of quantum characteristic and quantum flatness for arbitrary rings. More generally, we develop the theory of quantum integers in a ring and show that the hypothesis of quantum flatness together with positive quantum…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
While quantum computing holds immense potential for tackling previously intractable problems, its current practicality remains limited. A critical aspect of realizing quantum utility is the ability to efficiently interface with data from…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two…
This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning, specifically the ZX-calculus, to practical…
These results stem from a course on ring theory. Quantum planes are rings in two variables $x$ and $y$ such that $yx=qxy$ where $q$ is a nonzero constant. When $q=1$ a quantum plane is simply a commutative polynomial ring in two variables.…
We describe the notion of a quantum family of maps of a quantum space and that of a quantum commutant of such a family. Quantum commutants are quantum semigroups defined by a certain universal property. We give a few examples of these…
We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance.
We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator…
Phase is a basic ingredient for quantum states since quantum mechanics uses complex numbers to describe quantum states. In this letter, we introduce a rigorous framework to quantify the phase of quantum states. To do so, we regard phase as…
There has been no lack of coverage in the past few years in scientific journals of the topic of quantum computation. Rightly so, as this is a novel idea with--so far--at least one very important practical application (prime factorisation)…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
We present a method for optimizing quantum circuits architecture. The method is based on the notion of "quantum comb", which describes a circuit board in which one can insert variable subcircuits. The method allows one to efficiently…
Integrable quantum computation is defined as quantum computing via the integrable condition, in which two-qubit gates are either nontrivial unitary solutions of the Yang--Baxter equation or the Swap gate (permutation). To make the…